Exact critical bubble free energy and the effectiveness of effective potential approximations

David E. Brahm; Clarence L. Y. Lee

doi:10.1103/PhysRevD.49.4094

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Exact critical bubble free energy and the effectiveness of effective potential approximations

David E. Brahm^*

Clarence L. Y. Lee^†

Carnegie Mellon, Pittsburgh, Pennsylvania 15213

California Institute of Technology, Pasadena, California 91125

^*Electronic address: brahm@fermi.phys.cmu.edu
^†Electronic address: lee@theory3.caltech.edu

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Phys. Rev. D 49, 4094 – Published 15 April, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.4094

Abstract

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate $F_{c} (T)$ , the free energy of a critical bubble configuration. $F_{c} (T)$ is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when $V^{''} < 0$ . We test different effective potential approximations at one loop. The agreement is best if one pulls a factor $\frac{μ^{4}}{T^{4}}$ into the decay rate prefactor [where $μ^{2} = V^{''} (φ_{f})$ ], and takes the real part of the effective potential in the region $V^{''} < 0$ . We perform a similar analysis on the one-dimensional kink.

References (17)

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[c1] E. Weinberg, Phys. Rev. D 47, 4614 (1993)

[c2] S. Coleman, Phys. Rev. D 15, 2929 (1977) ibid.16, 1248(E) (1977) C. G. Callan and S. Coleman, ibid. 16, 1762 (1977) S. Coleman, The Uses of Instantons, Proceedings of 1977 International School of Subnuclear Physics, Ettore Majorana, edited by A. Zichichi (Plenum, New York, 1979) [reprinted in Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985)]

[c3] I. Affleck, Phys. Rev. Lett. 46, 388 (1981)

[c4] J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 31, 688 (1959) J. S. Langer, Ann. Phys. (N.Y.) 41, 108 (1967) ibid.54, 258 (1969) M. B. Voloshin, I. Y. Kobzarev, and L. B. Okun', Yad. Fiz. 20, 1229 (1974) [Sov. J. Nucl. Phys. 20, 644 (1975)] P. H. Frampton, Phys. Rev. D 15, 2922 (1977) A. D. Linde, Phys. Lett. 70B, 306 (1977) ibid.100B, 37 (1981) Nucl. Phys. B216, 421 (1983) ibid.B223, 544(E) (1983) O. J. P. Éboli and G. C. Marques, Rev. Bras. Fis. 16, 147 (1986)

[c5] M. Gleiser, G. C. Marques, and R. O. Ramos, Phys. Rev. D 48, 1571 (1993)

[c6] L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974)

[c7] H. Haber and H. A. Weldon, J. Math. Phys. 23, 1852 (1982)

[c8] C. L. Y. Lee, following paper, Phys. Rev. D 49, xxxx (1994)

[c9] C. G. Boyd et al., Phys. Rev. D 48, 4952 (1993)

[c10] L.-H. Chan, Phys. Rev. Lett. 54, 1222 (1985) ibid.56, 404(E) (1986)

[c11] I. Moss, D. Toms, and A. Wright, Phys. Rev. D 46, 1671 (1992)

[c12] M. Dine et al., Phys. Rev. D 46, 550 (1992) Phys. Lett. B 283, 319 (1992)

[c13] T.-P. Cheng and L.-F. Li, Gauge Theory of Elementary Particle Physics (Oxford University Press, Oxford, England, 1984)

[c14] Andrei Linde (private communication)

[c15] S. Dodelson and B. Gradwohl, Nucl. Phys. B400, 435 (1993)

[c16] R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4114 (1974) ibid.10, 4130 (1974) R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1987), Secs. 5.3-5.4

[c17] I. Ventura, Phys. Rev. B 24, 2812 (1981) C. Aragão de Carvalho et al., Phys. Rev. D 31, 1411 (1985) , Nucl. Phys. B265, 45 (1986) D. Bazeia et al., Z. Phys. C 46, 457 (1990)

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Exact critical bubble free energy and the effectiveness of effective potential approximations

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